Yes a ferroresonant unit.
Yup!
You can use it as is, but be aware that it essentially is a close to constant power transformer, giving a reasonably constant current output up to the open circuit voltage.
Nope: that would be closer to true if it were a shunted (split) transformer without the resonant winding. But that's more like constant impedance, not constant power. AFAIK, there's no such thing as a constant power transformer, not without some fancy mag amp trickery anyway.
You will also find that it is close to constant power draw on the input side as well, as it tends to run warm. As a battery charger for wet lead acid cells it is perfect, as it charges at a high current till the battery is close to full, then it keeps the voltage constant till the cell is just entering the hydrogen generating region when fully charged. This stirs the electrolyte and means the cells last a long time even in this high current use.
You can knock out the magnetic shunts and remove the capacitor and then it will be usable as a regular transformer.
...Maybe you typed 'power' when you were thinking 'voltage'?
In any case, what's going on is, the secondary side is held on the verge of magnetic saturation. Flux is volts times time, so as long as the frequency stays constant, the average voltage must also be limited. The shunts provide some isolation (loose coupling) between primary and secondary, and the capacitor winding is designed with a particular inductance (the secondary side may be gapped, I'm not sure) so that it resonates at line frequency. Normally, when something is resonant (at a high Q factor), the voltage and current just keep building up until balanced by losses, but in this case, the amplitude causes saturation first. This reduces the average inductance, raising the resonant frequency slightly above line frequency. Depending on load (i.e., how much excess voltage gets shunted by saturation), the amount of shift varies; it should be designed so that, between open circuit and rated load, and with an input of +/-10%, the output voltage remains within a 5% margin, or something like that.
The capacitor also helps smooth the waveform; a saturating sine wave looks like it's being shorted out on the tail (imagine a TRIAC phase control waveform, but instead of passing voltage for some fraction of the tail of the cycle, it gets shunted instead), but the capacitor forces the voltage up a little bit. The waveform will still be lopsided, so if you need really clean AC, some harmonic filtering might be desirable. For DC rectifiers, it's no problem of course.
Because of the magnetic shunts, the primary side power factor is quite poor: inductive. (It won't be especially distorted, though, even with a rectifier load.) If you want to minimize current draw, you could add some PFC capacitors. But beware they won't be friendly to switch contacts...
Tim